Abstract
This paper focuses on reconstruction of dynamic velocity and displacement from seismic acceleration signal. For conventional time-domain approaches or frequency-domain approaches, due to initial values and non-negligible noise in the acceleration signal, drift and deviation in velocity and displacement are inevitable. To deal with this deficiency, this paper develops a Walsh transform and Empirical Mode Decomposition (EMD)-based integral algorithm, or WATEBI in short. In the WATEBI algorithm, the Walsh transform is employed to realize vibration signal reconstruction. Next, the EMD method is used to eliminate the residual in the reconstructed signal. Finally, the trend term in velocity and displacement is removed by linear least-squares fit. This algorithm can be straightforwardly implemented by an ordinary computer. Reconstructed displacements and velocities from vibration of a simulated single-degree-of-freedom system and two-site measured ground motions in earthquakes validated the robustness and adaptiveness of this algorithm. It can be also applied to many other areas, like mechanical engineering and ocean engineering.
Highlights
With the rapid development of modern science and technology, the research on mechanical and structural vibration has promoted great advances in numerous engineering fields and areas, such as aerospace engineering, bridge engineering, earthquake engineering and offshore engineering [1,2].In mechanical engineering, vibration tests have attracted considerable attention, as they are of significant value for the health monitoring of machinery [3], including system operational reliability and mechanical breakdown detection
This paper proposes a Walsh Transform and Empirical Model Decomposition (EMD)-based
The vibration signal can be decomposed into several intrinsic mode functions (IMF) and a residual term shown as Equation (3)
Summary
With the rapid development of modern science and technology, the research on mechanical and structural vibration has promoted great advances in numerous engineering fields and areas, such as aerospace engineering, bridge engineering, earthquake engineering and offshore engineering [1,2]. The numerical scheme can be divided into two categories, time-domain integral [5] and frequency-domain conversion [7] The former includes known methods like trapezoid formula, Simpson’s rule, Newton-Cotes formula and first to Nth-order integral operator based on the Runge-Kutta algorithm. Many attempts have been proposed to improve the rationality and accuracy of the aforementioned methods These attempts are categorized into three classes of integral approaches, the time-domain polynomial fitting to remove the trend error [14], the band-pass filtering method [15], and FFT implementation with low-frequency cutoff and attenuation attempts [16,17,18], have demonstrated their good applicability in engineering problems. The other two cases are seismic recordings including ground acceleration, velocity and displacement, respectively, measured in two typical earthquakes
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